Point interactions in a strip

Pavel Exner R Gawlista P eba M Tater

TBD mathscidoc:1910.43053

annals of physics, 252, (1), 133-179, 1996.11
We study the behavior of a quantum particle confined to a hard-wall strip of a constant width in which there is a finite number<i>N</i>of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's formula, we analyze its spectral and scattering properties. The bound state problem is analogous to that of point interactions in the plane: since a two-dimensional point interaction is never repulsive, there are<i>m</i>discrete eigenvalues, 1<i>m</i><i>N</i>, the lowest of which is nondegenerate. On the other hand, due to the presence of the boundary the point interactions give rise to infinite series of resonances; if the coupling is weak they approach the thresholds of higher transverse modes. We derive also spectral and scattering properties for point perturbations in several related models: a cylindrical surface, both of a finite and of an infinite height, threaded by a magnetic flux, and a straight strip which
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  title={Point interactions in a strip},
  author={Pavel Exner, R Gawlista, P eba, and M Tater},
  booktitle={annals of physics},
Pavel Exner, R Gawlista, P eba, and M Tater. Point interactions in a strip. 1996. Vol. 252. In annals of physics. pp.133-179. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020123159146477582.
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